Import Question JSON

Current Question (ID: 19645)

Question:

$\text{A steel rail of length } 5 \text{ m and cross-sectional area } 40 \text{ cm}^2 \text{ is rigidly fixed at both ends, preventing it from expanding when the temperature rises by } 10^\circ \text{C.}$ $\text{Given that the coefficient of linear expansion of steel is } 1.2 \times 10^{-5} \text{ K}^{-1} \text{ and its Young's modulus is } 2 \times 10^{11} \text{ Nm}^{-2}, \text{ the approximate force developed in the rail is:}$

Options:

1. $1.2 \times 10^9 \text{ N}$
2. $3 \times 10^{-5} \text{ N}$
3. $2 \times 10^7 \text{ N}$
4. $1 \times 10^5 \text{ N}$

Solution:

$\text{Hint: } Y = \frac{\text{stress}}{\text{strain}}$ $\text{Step: Find the approximate force developed in the rail.}$ $F = Y A \alpha \Delta T$ $\Rightarrow F = 2 \times 10^{11} \times 40 \times 10^{-4} \times 1.2 \times 10^{-5} \times 10$ $\Rightarrow F = 9.6 \times 10^4 \text{ N} = 10 \times 10^4 \text{ N} \approx 1.0 \times 10^5 \text{ N}$ $\text{Hence, option (4) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}